Q: Does cropping FF (to ap-sc, for example) change DOF when displayed at the same sizes? Because I think you used to hold the position that it does not.

You missed the point!

Does cropping FF (to ap-sc, for example) change DOFwhen displayed at the same sizes?

To crop and then display at the same size the magnification must change and therefore the appearance of DOF will change!

Simple question how can it.?

The lens projects an image onto the film plane that image is the same whatever sensor is behind it

look at it this way assume we have a camera with interchangeable backs.

We put a 50mm f4 lens on the camera on a tripod with a FF back on it and take a picture.

we then do nothing but change the back to a sensor 1/2 the size and take another picture.

if we superimpose the two images on-top of each other will the be different in any way shape or form where they overlap?

The overlapping parts are absolutely identical AND HAVE DIFFERENT DEPTH OF FIELD.

Surely if we’ve overlapped the identical parts of the image they now are the same size and as such must be viewed at the same size and have the same DoF.?

You could take either image and re-present it at a new size and therefore change the DoF.

Therefore the idea the sensor size directly defines DoF is untrue.

Like most things the truth is more complex than the simple analogies used everyday.

A 6 Mp FF camera can never hove a narrower DoF than a 24Mp asp-c camera (with the same lens) . is this a foolish statement ?

My thought are you coudl never alter the FF image to the point where is showed smaller DoF than teh aps-c before hte lack of resolution destroyed the image.

theory being ff -> aps-c = 1.5 Vs 6 MP ->24 mP = 4

How so ? Because what I just typed sounds nuts.

Lets take your 50mm f/4 and focus it at infinity. We have a subject at 25m.

So the circle size is 50 x 50 / 4 * 25,000 = 0.025mm. Does that look in focus or out of focus ?The size at which what is not in perfect focus is noticeably out of focus depends on the size of the image. That size circle looks very different indistinguishable from a point on medium format and an enormous smudge on a Q. If we zoomed in enough on the medium format we can see it is out of focus. D of F is the zone which is out of focus but not noticeably so. You can notice a circle in a crop of an image which you don't notice when looking at the whole image.

All true except the lens has a defined registration distance you can never alter the projected size

So if the Distance is constant and the Circle Size is constant then what can alter the DoF?

The Circle will be 0,025 the distance will be 45.6 the image cast will always be the same , how much of that projected image you capture can either be defined by the sensor size or later by cropping both of which will define the viewing size.